Analysis of 111/999 NHS calls and 111 online reports
Quentin Leclerc, Emily Nightingale, Samuel Abbott & Thibaut Jombart, for CMMID
Monday 25 May 2020
1 Data preparation
1.1 Outline
Load scripts: loads libraries and useful scripts used in the analyses; all
.Rfiles contained inscriptsat the root of the factory are automatically loadedLoad data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.
1.2 Load packages
library(reportfactory)
library(here)
library(rio)
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)1.3 Load scripts
These scripts will load:
- all scripts stored as
.Rfiles inside/scripts/ - all scripts stored as
.Rfiles inside/src/
These scripts also contain routines to access the latest clean encrypted data (see next section).
1.4 Load clean data
We import the latest NHS pathways data:
x <- import_pathways() %>%
as_tibble()
x
## [90m# A tibble: 116,283 x 9[39m
## site_type date sex age ccg_code ccg_name count postcode nhs_region
## [3m[90m<chr>[39m[23m [3m[90m<date>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<int>[39m[23m [3m[90m<chr>[39m[23m [3m[90m<chr>[39m[23m
## [90m 1[39m 111 2020-03-18 female 0-18 e380000… nhs_bar… 35 rm13ae london
## [90m 2[39m 111 2020-03-18 female 0-18 e380000… nhs_bed… 27 mk454hr east_of_e…
## [90m 3[39m 111 2020-03-18 female 0-18 e380000… nhs_bla… 9 bb12fd north_west
## [90m 4[39m 111 2020-03-18 female 0-18 e380000… nhs_bro… 11 br33ql london
## [90m 5[39m 111 2020-03-18 female 0-18 e380000… nhs_can… 9 ws111jp midlands
## [90m 6[39m 111 2020-03-18 female 0-18 e380000… nhs_cit… 12 n15lz london
## [90m 7[39m 111 2020-03-18 female 0-18 e380000… nhs_enf… 7 en40dy london
## [90m 8[39m 111 2020-03-18 female 0-18 e380000… nhs_ham… 6 dl62uu north_eas…
## [90m 9[39m 111 2020-03-18 female 0-18 e380000… nhs_har… 24 ts232la north_eas…
## [90m10[39m 111 2020-03-18 female 0-18 e380000… nhs_kin… 6 kt11eu london
## [90m# … with 116,273 more rows[39mWe also import demographics data for NHS regions in England, used later in our analysis:
path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))
nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
## nhs_region variable value
## 1 North West 0-18 0.22538599
## 2 North East and Yorkshire 0-18 0.21876449
## 3 Midlands 0-18 0.22564656
## 4 East of England 0-18 0.22810783
## 5 London 0-18 0.23764782
## 6 South East 0-18 0.22458811
## 7 South West 0-18 0.20799797
## 8 North West 19-69 0.64274078
## 9 North East and Yorkshire 19-69 0.64437753
## 10 Midlands 19-69 0.63876675
## 11 East of England 19-69 0.63034229
## 12 London 19-69 0.67820084
## 13 South East 19-69 0.63267336
## 14 South West 19-69 0.63176131
## 15 North West 70-120 0.13187323
## 16 North East and Yorkshire 70-120 0.13685797
## 17 Midlands 70-120 0.13558669
## 18 East of England 70-120 0.14154988
## 19 London 70-120 0.08415135
## 20 South East 70-120 0.14273853
## 21 South West 70-120 0.16024072Finally, we import publically available deaths per NHS region:
dth <- import_deaths() %>%
mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))
#truncation to account for reporting delay
delay_max <- 21
dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
## date_report nhs_region deaths
## 1 2020-03-01 East of England 0
## 2 2020-03-02 East of England 1
## 3 2020-03-03 East of England 0
## 4 2020-03-04 East of England 0
## 5 2020-03-05 East of England 0
## 6 2020-03-06 East of England 1
## 7 2020-03-07 East of England 0
## 8 2020-03-08 East of England 0
## 9 2020-03-09 East of England 1
## 10 2020-03-10 East of England 0
## 11 2020-03-11 East of England 0
## 12 2020-03-12 East of England 0
## 13 2020-03-13 East of England 1
## 14 2020-03-14 East of England 2
## 15 2020-03-15 East of England 2
## 16 2020-03-16 East of England 1
## 17 2020-03-17 East of England 1
## 18 2020-03-18 East of England 5
## 19 2020-03-19 East of England 4
## 20 2020-03-20 East of England 2
## 21 2020-03-21 East of England 11
## 22 2020-03-22 East of England 11
## 23 2020-03-23 East of England 11
## 24 2020-03-24 East of England 19
## 25 2020-03-25 East of England 26
## 26 2020-03-26 East of England 36
## 27 2020-03-27 East of England 38
## 28 2020-03-28 East of England 28
## 29 2020-03-29 East of England 42
## 30 2020-03-30 East of England 45
## 31 2020-03-31 East of England 70
## 32 2020-04-01 East of England 61
## 33 2020-04-02 East of England 64
## 34 2020-04-03 East of England 80
## 35 2020-04-04 East of England 71
## 36 2020-04-05 East of England 76
## 37 2020-04-06 East of England 71
## 38 2020-04-07 East of England 92
## 39 2020-04-08 East of England 111
## 40 2020-04-09 East of England 87
## 41 2020-04-10 East of England 74
## 42 2020-04-11 East of England 91
## 43 2020-04-12 East of England 101
## 44 2020-04-13 East of England 77
## 45 2020-04-14 East of England 61
## 46 2020-04-15 East of England 82
## 47 2020-04-16 East of England 74
## 48 2020-04-17 East of England 86
## 49 2020-04-18 East of England 63
## 50 2020-04-19 East of England 66
## 51 2020-04-20 East of England 66
## 52 2020-04-21 East of England 74
## 53 2020-04-22 East of England 66
## 54 2020-04-23 East of England 49
## 55 2020-04-24 East of England 64
## 56 2020-04-25 East of England 54
## 57 2020-04-26 East of England 48
## 58 2020-04-27 East of England 46
## 59 2020-04-28 East of England 58
## 60 2020-04-29 East of England 32
## 61 2020-04-30 East of England 43
## 62 2020-05-01 East of England 49
## 63 2020-05-02 East of England 29
## 64 2020-05-03 East of England 41
## 65 2020-05-04 East of England 19
## 66 2020-05-05 East of England 35
## 67 2020-05-06 East of England 28
## 68 2020-05-07 East of England 33
## 69 2020-05-08 East of England 30
## 70 2020-05-09 East of England 26
## 71 2020-05-10 East of England 21
## 72 2020-05-11 East of England 18
## 73 2020-05-12 East of England 21
## 74 2020-05-13 East of England 27
## 75 2020-05-14 East of England 25
## 76 2020-05-15 East of England 18
## 77 2020-05-16 East of England 24
## 78 2020-05-17 East of England 15
## 79 2020-05-18 East of England 16
## 80 2020-05-19 East of England 14
## 81 2020-05-20 East of England 21
## 82 2020-05-21 East of England 17
## 83 2020-05-22 East of England 7
## 84 2020-05-23 East of England 2
## 85 2020-03-01 London 0
## 86 2020-03-02 London 0
## 87 2020-03-03 London 0
## 88 2020-03-04 London 0
## 89 2020-03-05 London 0
## 90 2020-03-06 London 1
## 91 2020-03-07 London 1
## 92 2020-03-08 London 0
## 93 2020-03-09 London 1
## 94 2020-03-10 London 0
## 95 2020-03-11 London 7
## 96 2020-03-12 London 6
## 97 2020-03-13 London 10
## 98 2020-03-14 London 14
## 99 2020-03-15 London 10
## 100 2020-03-16 London 17
## 101 2020-03-17 London 25
## 102 2020-03-18 London 31
## 103 2020-03-19 London 25
## 104 2020-03-20 London 45
## 105 2020-03-21 London 49
## 106 2020-03-22 London 54
## 107 2020-03-23 London 63
## 108 2020-03-24 London 86
## 109 2020-03-25 London 112
## 110 2020-03-26 London 130
## 111 2020-03-27 London 129
## 112 2020-03-28 London 122
## 113 2020-03-29 London 147
## 114 2020-03-30 London 148
## 115 2020-03-31 London 180
## 116 2020-04-01 London 201
## 117 2020-04-02 London 189
## 118 2020-04-03 London 196
## 119 2020-04-04 London 229
## 120 2020-04-05 London 194
## 121 2020-04-06 London 198
## 122 2020-04-07 London 219
## 123 2020-04-08 London 236
## 124 2020-04-09 London 202
## 125 2020-04-10 London 168
## 126 2020-04-11 London 175
## 127 2020-04-12 London 156
## 128 2020-04-13 London 165
## 129 2020-04-14 London 142
## 130 2020-04-15 London 142
## 131 2020-04-16 London 138
## 132 2020-04-17 London 99
## 133 2020-04-18 London 101
## 134 2020-04-19 London 102
## 135 2020-04-20 London 94
## 136 2020-04-21 London 93
## 137 2020-04-22 London 108
## 138 2020-04-23 London 77
## 139 2020-04-24 London 71
## 140 2020-04-25 London 57
## 141 2020-04-26 London 53
## 142 2020-04-27 London 51
## 143 2020-04-28 London 43
## 144 2020-04-29 London 43
## 145 2020-04-30 London 39
## 146 2020-05-01 London 41
## 147 2020-05-02 London 40
## 148 2020-05-03 London 35
## 149 2020-05-04 London 29
## 150 2020-05-05 London 25
## 151 2020-05-06 London 34
## 152 2020-05-07 London 35
## 153 2020-05-08 London 29
## 154 2020-05-09 London 22
## 155 2020-05-10 London 25
## 156 2020-05-11 London 16
## 157 2020-05-12 London 16
## 158 2020-05-13 London 16
## 159 2020-05-14 London 20
## 160 2020-05-15 London 17
## 161 2020-05-16 London 13
## 162 2020-05-17 London 15
## 163 2020-05-18 London 9
## 164 2020-05-19 London 12
## 165 2020-05-20 London 18
## 166 2020-05-21 London 10
## 167 2020-05-22 London 5
## 168 2020-05-23 London 2
## 169 2020-03-01 Midlands 0
## 170 2020-03-02 Midlands 0
## 171 2020-03-03 Midlands 1
## 172 2020-03-04 Midlands 0
## 173 2020-03-05 Midlands 0
## 174 2020-03-06 Midlands 0
## 175 2020-03-07 Midlands 0
## 176 2020-03-08 Midlands 3
## 177 2020-03-09 Midlands 1
## 178 2020-03-10 Midlands 0
## 179 2020-03-11 Midlands 2
## 180 2020-03-12 Midlands 6
## 181 2020-03-13 Midlands 5
## 182 2020-03-14 Midlands 4
## 183 2020-03-15 Midlands 5
## 184 2020-03-16 Midlands 11
## 185 2020-03-17 Midlands 8
## 186 2020-03-18 Midlands 13
## 187 2020-03-19 Midlands 8
## 188 2020-03-20 Midlands 28
## 189 2020-03-21 Midlands 13
## 190 2020-03-22 Midlands 31
## 191 2020-03-23 Midlands 33
## 192 2020-03-24 Midlands 41
## 193 2020-03-25 Midlands 48
## 194 2020-03-26 Midlands 64
## 195 2020-03-27 Midlands 72
## 196 2020-03-28 Midlands 89
## 197 2020-03-29 Midlands 92
## 198 2020-03-30 Midlands 90
## 199 2020-03-31 Midlands 123
## 200 2020-04-01 Midlands 140
## 201 2020-04-02 Midlands 142
## 202 2020-04-03 Midlands 124
## 203 2020-04-04 Midlands 150
## 204 2020-04-05 Midlands 164
## 205 2020-04-06 Midlands 140
## 206 2020-04-07 Midlands 123
## 207 2020-04-08 Midlands 185
## 208 2020-04-09 Midlands 138
## 209 2020-04-10 Midlands 127
## 210 2020-04-11 Midlands 142
## 211 2020-04-12 Midlands 138
## 212 2020-04-13 Midlands 120
## 213 2020-04-14 Midlands 116
## 214 2020-04-15 Midlands 147
## 215 2020-04-16 Midlands 101
## 216 2020-04-17 Midlands 118
## 217 2020-04-18 Midlands 115
## 218 2020-04-19 Midlands 91
## 219 2020-04-20 Midlands 107
## 220 2020-04-21 Midlands 86
## 221 2020-04-22 Midlands 77
## 222 2020-04-23 Midlands 102
## 223 2020-04-24 Midlands 77
## 224 2020-04-25 Midlands 72
## 225 2020-04-26 Midlands 81
## 226 2020-04-27 Midlands 74
## 227 2020-04-28 Midlands 68
## 228 2020-04-29 Midlands 53
## 229 2020-04-30 Midlands 53
## 230 2020-05-01 Midlands 64
## 231 2020-05-02 Midlands 51
## 232 2020-05-03 Midlands 50
## 233 2020-05-04 Midlands 60
## 234 2020-05-05 Midlands 58
## 235 2020-05-06 Midlands 56
## 236 2020-05-07 Midlands 48
## 237 2020-05-08 Midlands 34
## 238 2020-05-09 Midlands 37
## 239 2020-05-10 Midlands 41
## 240 2020-05-11 Midlands 32
## 241 2020-05-12 Midlands 45
## 242 2020-05-13 Midlands 38
## 243 2020-05-14 Midlands 32
## 244 2020-05-15 Midlands 38
## 245 2020-05-16 Midlands 34
## 246 2020-05-17 Midlands 30
## 247 2020-05-18 Midlands 33
## 248 2020-05-19 Midlands 31
## 249 2020-05-20 Midlands 31
## 250 2020-05-21 Midlands 26
## 251 2020-05-22 Midlands 14
## 252 2020-05-23 Midlands 7
## 253 2020-03-01 North East and Yorkshire 0
## 254 2020-03-02 North East and Yorkshire 0
## 255 2020-03-03 North East and Yorkshire 0
## 256 2020-03-04 North East and Yorkshire 0
## 257 2020-03-05 North East and Yorkshire 0
## 258 2020-03-06 North East and Yorkshire 0
## 259 2020-03-07 North East and Yorkshire 0
## 260 2020-03-08 North East and Yorkshire 0
## 261 2020-03-09 North East and Yorkshire 0
## 262 2020-03-10 North East and Yorkshire 0
## 263 2020-03-11 North East and Yorkshire 0
## 264 2020-03-12 North East and Yorkshire 0
## 265 2020-03-13 North East and Yorkshire 0
## 266 2020-03-14 North East and Yorkshire 0
## 267 2020-03-15 North East and Yorkshire 2
## 268 2020-03-16 North East and Yorkshire 3
## 269 2020-03-17 North East and Yorkshire 1
## 270 2020-03-18 North East and Yorkshire 2
## 271 2020-03-19 North East and Yorkshire 6
## 272 2020-03-20 North East and Yorkshire 5
## 273 2020-03-21 North East and Yorkshire 6
## 274 2020-03-22 North East and Yorkshire 7
## 275 2020-03-23 North East and Yorkshire 9
## 276 2020-03-24 North East and Yorkshire 7
## 277 2020-03-25 North East and Yorkshire 18
## 278 2020-03-26 North East and Yorkshire 21
## 279 2020-03-27 North East and Yorkshire 28
## 280 2020-03-28 North East and Yorkshire 35
## 281 2020-03-29 North East and Yorkshire 38
## 282 2020-03-30 North East and Yorkshire 64
## 283 2020-03-31 North East and Yorkshire 60
## 284 2020-04-01 North East and Yorkshire 67
## 285 2020-04-02 North East and Yorkshire 74
## 286 2020-04-03 North East and Yorkshire 99
## 287 2020-04-04 North East and Yorkshire 104
## 288 2020-04-05 North East and Yorkshire 92
## 289 2020-04-06 North East and Yorkshire 95
## 290 2020-04-07 North East and Yorkshire 102
## 291 2020-04-08 North East and Yorkshire 107
## 292 2020-04-09 North East and Yorkshire 111
## 293 2020-04-10 North East and Yorkshire 117
## 294 2020-04-11 North East and Yorkshire 98
## 295 2020-04-12 North East and Yorkshire 84
## 296 2020-04-13 North East and Yorkshire 94
## 297 2020-04-14 North East and Yorkshire 107
## 298 2020-04-15 North East and Yorkshire 95
## 299 2020-04-16 North East and Yorkshire 103
## 300 2020-04-17 North East and Yorkshire 86
## 301 2020-04-18 North East and Yorkshire 95
## 302 2020-04-19 North East and Yorkshire 87
## 303 2020-04-20 North East and Yorkshire 100
## 304 2020-04-21 North East and Yorkshire 76
## 305 2020-04-22 North East and Yorkshire 83
## 306 2020-04-23 North East and Yorkshire 62
## 307 2020-04-24 North East and Yorkshire 72
## 308 2020-04-25 North East and Yorkshire 68
## 309 2020-04-26 North East and Yorkshire 63
## 310 2020-04-27 North East and Yorkshire 65
## 311 2020-04-28 North East and Yorkshire 57
## 312 2020-04-29 North East and Yorkshire 69
## 313 2020-04-30 North East and Yorkshire 56
## 314 2020-05-01 North East and Yorkshire 64
## 315 2020-05-02 North East and Yorkshire 48
## 316 2020-05-03 North East and Yorkshire 39
## 317 2020-05-04 North East and Yorkshire 48
## 318 2020-05-05 North East and Yorkshire 40
## 319 2020-05-06 North East and Yorkshire 50
## 320 2020-05-07 North East and Yorkshire 41
## 321 2020-05-08 North East and Yorkshire 38
## 322 2020-05-09 North East and Yorkshire 43
## 323 2020-05-10 North East and Yorkshire 39
## 324 2020-05-11 North East and Yorkshire 28
## 325 2020-05-12 North East and Yorkshire 25
## 326 2020-05-13 North East and Yorkshire 27
## 327 2020-05-14 North East and Yorkshire 28
## 328 2020-05-15 North East and Yorkshire 30
## 329 2020-05-16 North East and Yorkshire 35
## 330 2020-05-17 North East and Yorkshire 26
## 331 2020-05-18 North East and Yorkshire 26
## 332 2020-05-19 North East and Yorkshire 27
## 333 2020-05-20 North East and Yorkshire 20
## 334 2020-05-21 North East and Yorkshire 29
## 335 2020-05-22 North East and Yorkshire 19
## 336 2020-05-23 North East and Yorkshire 8
## 337 2020-03-01 North West 0
## 338 2020-03-02 North West 0
## 339 2020-03-03 North West 0
## 340 2020-03-04 North West 0
## 341 2020-03-05 North West 1
## 342 2020-03-06 North West 0
## 343 2020-03-07 North West 0
## 344 2020-03-08 North West 1
## 345 2020-03-09 North West 0
## 346 2020-03-10 North West 0
## 347 2020-03-11 North West 0
## 348 2020-03-12 North West 2
## 349 2020-03-13 North West 3
## 350 2020-03-14 North West 1
## 351 2020-03-15 North West 4
## 352 2020-03-16 North West 2
## 353 2020-03-17 North West 4
## 354 2020-03-18 North West 6
## 355 2020-03-19 North West 6
## 356 2020-03-20 North West 10
## 357 2020-03-21 North West 11
## 358 2020-03-22 North West 13
## 359 2020-03-23 North West 15
## 360 2020-03-24 North West 21
## 361 2020-03-25 North West 20
## 362 2020-03-26 North West 29
## 363 2020-03-27 North West 35
## 364 2020-03-28 North West 27
## 365 2020-03-29 North West 46
## 366 2020-03-30 North West 66
## 367 2020-03-31 North West 52
## 368 2020-04-01 North West 85
## 369 2020-04-02 North West 95
## 370 2020-04-03 North West 94
## 371 2020-04-04 North West 98
## 372 2020-04-05 North West 102
## 373 2020-04-06 North West 100
## 374 2020-04-07 North West 133
## 375 2020-04-08 North West 123
## 376 2020-04-09 North West 118
## 377 2020-04-10 North West 115
## 378 2020-04-11 North West 135
## 379 2020-04-12 North West 126
## 380 2020-04-13 North West 125
## 381 2020-04-14 North West 130
## 382 2020-04-15 North West 114
## 383 2020-04-16 North West 133
## 384 2020-04-17 North West 96
## 385 2020-04-18 North West 112
## 386 2020-04-19 North West 70
## 387 2020-04-20 North West 80
## 388 2020-04-21 North West 75
## 389 2020-04-22 North West 80
## 390 2020-04-23 North West 85
## 391 2020-04-24 North West 65
## 392 2020-04-25 North West 65
## 393 2020-04-26 North West 54
## 394 2020-04-27 North West 54
## 395 2020-04-28 North West 56
## 396 2020-04-29 North West 62
## 397 2020-04-30 North West 57
## 398 2020-05-01 North West 43
## 399 2020-05-02 North West 55
## 400 2020-05-03 North West 54
## 401 2020-05-04 North West 44
## 402 2020-05-05 North West 46
## 403 2020-05-06 North West 41
## 404 2020-05-07 North West 44
## 405 2020-05-08 North West 40
## 406 2020-05-09 North West 28
## 407 2020-05-10 North West 38
## 408 2020-05-11 North West 32
## 409 2020-05-12 North West 35
## 410 2020-05-13 North West 24
## 411 2020-05-14 North West 26
## 412 2020-05-15 North West 33
## 413 2020-05-16 North West 30
## 414 2020-05-17 North West 23
## 415 2020-05-18 North West 26
## 416 2020-05-19 North West 31
## 417 2020-05-20 North West 23
## 418 2020-05-21 North West 20
## 419 2020-05-22 North West 13
## 420 2020-05-23 North West 7
## 421 2020-03-01 South East 0
## 422 2020-03-02 South East 0
## 423 2020-03-03 South East 1
## 424 2020-03-04 South East 0
## 425 2020-03-05 South East 1
## 426 2020-03-06 South East 0
## 427 2020-03-07 South East 0
## 428 2020-03-08 South East 1
## 429 2020-03-09 South East 1
## 430 2020-03-10 South East 1
## 431 2020-03-11 South East 1
## 432 2020-03-12 South East 0
## 433 2020-03-13 South East 1
## 434 2020-03-14 South East 1
## 435 2020-03-15 South East 5
## 436 2020-03-16 South East 8
## 437 2020-03-17 South East 7
## 438 2020-03-18 South East 10
## 439 2020-03-19 South East 9
## 440 2020-03-20 South East 13
## 441 2020-03-21 South East 7
## 442 2020-03-22 South East 25
## 443 2020-03-23 South East 20
## 444 2020-03-24 South East 22
## 445 2020-03-25 South East 28
## 446 2020-03-26 South East 34
## 447 2020-03-27 South East 34
## 448 2020-03-28 South East 36
## 449 2020-03-29 South East 54
## 450 2020-03-30 South East 58
## 451 2020-03-31 South East 65
## 452 2020-04-01 South East 65
## 453 2020-04-02 South East 55
## 454 2020-04-03 South East 72
## 455 2020-04-04 South East 80
## 456 2020-04-05 South East 81
## 457 2020-04-06 South East 87
## 458 2020-04-07 South East 99
## 459 2020-04-08 South East 82
## 460 2020-04-09 South East 104
## 461 2020-04-10 South East 88
## 462 2020-04-11 South East 87
## 463 2020-04-12 South East 88
## 464 2020-04-13 South East 83
## 465 2020-04-14 South East 64
## 466 2020-04-15 South East 72
## 467 2020-04-16 South East 56
## 468 2020-04-17 South East 86
## 469 2020-04-18 South East 57
## 470 2020-04-19 South East 69
## 471 2020-04-20 South East 85
## 472 2020-04-21 South East 49
## 473 2020-04-22 South East 54
## 474 2020-04-23 South East 57
## 475 2020-04-24 South East 64
## 476 2020-04-25 South East 50
## 477 2020-04-26 South East 51
## 478 2020-04-27 South East 40
## 479 2020-04-28 South East 40
## 480 2020-04-29 South East 46
## 481 2020-04-30 South East 28
## 482 2020-05-01 South East 37
## 483 2020-05-02 South East 35
## 484 2020-05-03 South East 17
## 485 2020-05-04 South East 35
## 486 2020-05-05 South East 29
## 487 2020-05-06 South East 22
## 488 2020-05-07 South East 25
## 489 2020-05-08 South East 25
## 490 2020-05-09 South East 28
## 491 2020-05-10 South East 19
## 492 2020-05-11 South East 23
## 493 2020-05-12 South East 26
## 494 2020-05-13 South East 17
## 495 2020-05-14 South East 31
## 496 2020-05-15 South East 23
## 497 2020-05-16 South East 18
## 498 2020-05-17 South East 16
## 499 2020-05-18 South East 17
## 500 2020-05-19 South East 12
## 501 2020-05-20 South East 21
## 502 2020-05-21 South East 10
## 503 2020-05-22 South East 8
## 504 2020-05-23 South East 1
## 505 2020-03-01 South West 0
## 506 2020-03-02 South West 0
## 507 2020-03-03 South West 0
## 508 2020-03-04 South West 0
## 509 2020-03-05 South West 0
## 510 2020-03-06 South West 0
## 511 2020-03-07 South West 0
## 512 2020-03-08 South West 0
## 513 2020-03-09 South West 0
## 514 2020-03-10 South West 0
## 515 2020-03-11 South West 1
## 516 2020-03-12 South West 0
## 517 2020-03-13 South West 0
## 518 2020-03-14 South West 1
## 519 2020-03-15 South West 0
## 520 2020-03-16 South West 0
## 521 2020-03-17 South West 2
## 522 2020-03-18 South West 2
## 523 2020-03-19 South West 4
## 524 2020-03-20 South West 3
## 525 2020-03-21 South West 6
## 526 2020-03-22 South West 9
## 527 2020-03-23 South West 9
## 528 2020-03-24 South West 7
## 529 2020-03-25 South West 9
## 530 2020-03-26 South West 11
## 531 2020-03-27 South West 13
## 532 2020-03-28 South West 21
## 533 2020-03-29 South West 18
## 534 2020-03-30 South West 23
## 535 2020-03-31 South West 23
## 536 2020-04-01 South West 22
## 537 2020-04-02 South West 23
## 538 2020-04-03 South West 30
## 539 2020-04-04 South West 42
## 540 2020-04-05 South West 32
## 541 2020-04-06 South West 34
## 542 2020-04-07 South West 39
## 543 2020-04-08 South West 47
## 544 2020-04-09 South West 24
## 545 2020-04-10 South West 46
## 546 2020-04-11 South West 43
## 547 2020-04-12 South West 23
## 548 2020-04-13 South West 26
## 549 2020-04-14 South West 24
## 550 2020-04-15 South West 31
## 551 2020-04-16 South West 29
## 552 2020-04-17 South West 33
## 553 2020-04-18 South West 25
## 554 2020-04-19 South West 31
## 555 2020-04-20 South West 26
## 556 2020-04-21 South West 26
## 557 2020-04-22 South West 22
## 558 2020-04-23 South West 17
## 559 2020-04-24 South West 19
## 560 2020-04-25 South West 15
## 561 2020-04-26 South West 27
## 562 2020-04-27 South West 13
## 563 2020-04-28 South West 17
## 564 2020-04-29 South West 14
## 565 2020-04-30 South West 26
## 566 2020-05-01 South West 6
## 567 2020-05-02 South West 6
## 568 2020-05-03 South West 10
## 569 2020-05-04 South West 16
## 570 2020-05-05 South West 14
## 571 2020-05-06 South West 18
## 572 2020-05-07 South West 16
## 573 2020-05-08 South West 5
## 574 2020-05-09 South West 10
## 575 2020-05-10 South West 5
## 576 2020-05-11 South West 7
## 577 2020-05-12 South West 7
## 578 2020-05-13 South West 7
## 579 2020-05-14 South West 6
## 580 2020-05-15 South West 3
## 581 2020-05-16 South West 4
## 582 2020-05-17 South West 6
## 583 2020-05-18 South West 4
## 584 2020-05-19 South West 5
## 585 2020-05-20 South West 1
## 586 2020-05-21 South West 8
## 587 2020-05-22 South West 4
## 588 2020-05-23 South West 11.5 Completion date
We extract the completion date from the NHS Pathways file timestamp:
The completion date of the NHS Pathways data is Thursday 21 May 2020.
1.6 Add variables
We add the following variable:
day: an integer representing the number of days from the earliest data reported, used for modelling purposes; the first day is 0
1.7 Auxiliary functions
These are functions which will be used further in the analyses.
Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:
## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here
Rsq <- function(x) {
1 - (x$deviance / x$null.deviance)
}Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:
## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals
get_r <- function(model) {
## extract coefficients and conf int
out <- data.frame(r = coef(model)) %>%
rownames_to_column("var") %>%
cbind(confint(model)) %>%
filter(!grepl("day_of_week", var)) %>%
filter(grepl("day", var)) %>%
rename(lower_95 = "2.5 %",
upper_95 = "97.5 %") %>%
mutate(var = sub("day:", "", var))
## reconstruct values: intercept + region-coefficient
for (i in 2:nrow(out)) {
out[i, -1] <- out[1, -1] + out[i, -1]
}
## find the name of the intercept, restore regions names
out <- out %>%
mutate(nhs_region = model$xlevels$nhs_region) %>%
select(nhs_region, everything(), -var)
## find halving times
halving <- log(0.5) / out[,-1] %>%
rename(halving_t = r,
halving_t_lower_95 = lower_95,
halving_t_upper_95 = upper_95)
## set halving times with exclusion intervals to NA
no_halving <- out$lower_95 < 0 & out$upper_95 > 0
halving[no_halving, ] <- NA_real_
## return all data
cbind(out, halving)
}Functions used in the correlation analysis between NHS Pathways reports and deaths:
## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.
getcor <- function(x, ndx) {
return(cor(x$deaths[ndx],
x$note_lag[ndx],
use = "complete.obs",
method = "pearson"))
}
## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)
getboot <- function(x) {
result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000),
type = "bca")
return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
r = result$t0,
r_low = result$bca[4],
r_hi = result$bca[5]))
}Function to classify the day of the week into weekend, Monday, and the rest:
## Fn to add day of week
day_of_week <- function(df) {
df %>%
dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>%
dplyr::mutate(day_of_week = dplyr::case_when(
day_of_week %in% c("Sat", "Sun") ~ "weekend",
day_of_week %in% c("Mon") ~ "monday",
!(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
) %>%
factor(levels = c("rest_of_week", "monday", "weekend")))
}Custom color palettes, color scales, and vectors of colors:
2 Temporal trends in NHS Pathways reports
2.1 Outline
We look for temporal patterns in COVID-19 related 111/999 calls and 111 online reports. Analyses are broken down by NHS region. We also look for estimates of recent growth rate and associated doubling / halving time.
2.2 Reports by region over time
tab_date_region_all <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
dth %>%
mutate(trusted = case_when(date_report < max(dth$date_report)-delay_max ~ "Y",
date_report >= max(dth$date_report)-delay_max ~ "N"),
value = "Deaths",
vline = max(dth$date_report)-delay_max-1,
lab = "Truncated for reporting delay",
lab_pos_x = vline + 8,
lab_pos_y = 150,
lab_col = "darkgrey") %>%
rename(date = date_report,
n = deaths) %>%
bind_rows(
mutate(tab_date_region_all, value = "Reports",
trusted = "Y",
vline = as.Date("2020-03-23"),
lab = "Start of UK lockdown",
lab_pos_x = vline - 6,
lab_pos_y = 30000,
lab_col = "black")
) %>%
mutate(value = factor(value, levels = c("Reports","Deaths"))) -> dths_reports
plot_dth_report <-
ggplot(dths_reports, aes(date, n, colour = nhs_region)) +
# Add main points and lines, coloured by region and fade out deaths for excluded period
geom_point(aes(alpha = trusted)) +
geom_line(alpha = 0.2) +
geom_smooth(method = "loess", span = .5, color = "black") +
scale_colour_manual("", values = pal) +
scale_alpha_manual(values = c(0.3,1)) +
guides(alpha = F) +
# Add vertical markers for important dates with labels - different for each facet
ggnewscale::new_scale_colour() +
geom_vline(aes(xintercept = vline, col = value), lty = "solid") +
geom_text(aes(x = lab_pos_x, y = lab_pos_y, label = lab, col = value), size = 3) +
scale_colour_manual("",values = c("black","darkgrey"), guide = F) +
# Facet by deaths and reports
facet_grid(rows = vars(value), scales = "free_y", switch = "y") +
# Other formatting
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",strip.placement = "outside") +
rotate_x +
labs(x = NULL,
y = NULL)
plot_dth_report
2.3 Reports by region by age over time
We plot the number of 111/999 calls and 111 online reports by age, and the proportion of 111/999 calls and 111 online reports by age. In the second graph, the vertical lines indicate the proportion of individuals residing in the corresponding NHS region who belong to the corresponding age group.
tab_date_region_age_all <- x %>%
filter(!is.na(nhs_region),
age != "missing") %>%
group_by(date, nhs_region, age) %>%
summarise(n = sum(count))
tab_date_region_age_all %>%
ggplot(aes(x = date, y = n, fill = age)) +
geom_col(position = "stack") +
scale_fill_manual(values = age.pal) +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
axis.text.x = element_text(angle = 90, hjust = 1)) +
guides(fill = guide_legend(title = "Age", ncol = 3)) +
labs(x = NULL,
y = "Total daily reports by age") +
facet_wrap(~ nhs_region, ncol = 4)
tab_date_region_age_all <- tab_date_region_age_all %>%
group_by(date, nhs_region) %>%
summarise(tot = sum(n)) %>%
left_join(tab_date_region_age_all, by = c("date", "nhs_region")) %>%
mutate(prop_n = n/tot)
tab_date_region_age_all %>%
ggplot(aes(x = date, y = prop_n, color = age)) +
scale_color_manual(values = age.pal) +
geom_line() +
geom_point() +
geom_hline(data = nhs_region_pop, aes(yintercept = value, color = variable)) +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
axis.text.x = element_text(angle = 90, hjust = 1)) +
guides(color = guide_legend(title = "Age", ncol = 3)) +
labs(x = NULL,
y = "Proportion of daily reports by age") +
facet_wrap(~ nhs_region, ncol = 4)
2.4 Moving window model
We fit quasi-Poisson GLMs for 14-day windows to get growth rates over time.
## set moving time window (1/2/3 weeks)
w <- 14
# create empty df
r_all_sliding <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding <- bind_rows(r_all_sliding, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding <- r_all_sliding %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))We examine the evolution of the growth rate by region over time.
# plot
plot_growth <-
r_all_sliding %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)From the growth rate, we derive R and examine its value through time.
# plot
plot_R <-
r_all_sliding %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
# strip.text.x = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "",
override.aes = list(fill = NA)),
fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))
2.5 Moving window model - stratified by age
We repeat the above analysis, where we fit quasi-Poisson GLMs for 14-day windows to get growth rates over time, but apply this to each age group separately (0-18, 19-69, 70-120 years old).
We first run the analysis for 0-18 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_0_18 <- NULL
## make data for model
x_model_all_moving_0_18 <- x %>%
filter(!is.na(nhs_region),
age == "0-18") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_0_18$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_0_18 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_0_18 <- bind_rows(r_all_sliding_0_18, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_0_18 <- r_all_sliding_0_18 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_0_18 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)"
) +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_0_18 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)"
) +
scale_colour_manual(values = pal)
R <- r_all_sliding_0_18 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_0_18 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_0_18 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Then, we run the analysis for 19-69 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_19_69 <- NULL
## make data for model
x_model_all_moving_19_69 <- x %>%
filter(!is.na(nhs_region),
age == "19-69") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_19_69$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_19_69 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_19_69 <- bind_rows(r_all_sliding_19_69, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_19_69 <- r_all_sliding_19_69 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_19_69 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_19_69 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)"
) +
scale_colour_manual(values = pal)
R <- r_all_sliding_19_69 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_19_69 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_19_69 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Finally, we run the analysis for 70-120 years old.
## set moving time window (2 weeks)
w <- 14
# create empty df
r_all_sliding_70_120 <- NULL
## make data for model
x_model_all_moving_70_120 <- x %>%
filter(!is.na(nhs_region),
age == "70-120") %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving_70_120$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving_70_120 %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_70_120 <- bind_rows(r_all_sliding_70_120, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
#convert growth rates r to R0
r_all_sliding_70_120 <- r_all_sliding_70_120 %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_70_120 %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)"
) +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_70_120 %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_70_120 %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_70_120 %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
fig2_3_70_120 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)"))) We combine the estimated growth rates and effective reproduction numbers into a single figure.
ggpubr::ggarrange(fig2_3_0_18,
fig2_3_19_69,
fig2_3_70_120,
nrow = 3,
labels = "AUTO",
common.legend = TRUE,
legend = "bottom",
align = "hv") 
3 Comparison with deaths time series
3.1 Outline
We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.
Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.
3.2 Lagged correlation
We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.
First we join the NHS Pathways and death data, and aggregate over all England:
## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max
dth_trunc <- dth %>%
rename(date = date_report) %>%
filter(date <= trunc_date)
## join with notification data
all_data <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(count = sum(count, na.rm = T)) %>%
ungroup %>%
inner_join(dth_trunc,
by = c("date","nhs_region"))
all_tot <- all_data %>%
group_by(date) %>%
summarise(count = sum(count, na.rm = TRUE),
deaths = sum(deaths, na.rm = TRUE)) We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:
## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
## lag reports
summary <- all_tot %>%
mutate(note_lag = lag(count, i)) %>%
## calculate rank correlation and bootstrap CI
getboot(.) %>%
mutate(lag = i)
lag_cor <- bind_rows(lag_cor, summary)
}
cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
theme_bw() +
geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
geom_hline(yintercept = 0, lty = "longdash") +
geom_point() +
geom_line() +
labs(x = "Lag between NHS pathways and death data (days)",
y = "Pearson's correlation") +
large_txt
cor_vs_lag
This analysis suggests that the best lag is 16 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 16 days.
all_tot <- all_tot %>%
rename(date_death = date) %>%
mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
date_note = lag(date_death,16))
lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")
summary(lag_mod)
##
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -5.5040 -1.7684 -0.2302 2.0232 5.9304
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.683e+00 5.388e-02 105.47 < 2e-16 ***
## note_lag 7.235e-06 5.090e-07 14.22 2.48e-14 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for quasipoisson family taken to be 7.719516)
##
## Null deviance: 1791.25 on 29 degrees of freedom
## Residual deviance: 216.91 on 28 degrees of freedom
## (16 observations deleted due to missingness)
## AIC: NA
##
## Number of Fisher Scoring iterations: 4
exp(coefficients(lag_mod))
## (Intercept) note_lag
## 293.915663 1.000007
exp(confint(lag_mod))
## 2.5 % 97.5 %
## (Intercept) 264.220481 326.366718
## note_lag 1.000006 1.000008
Rsq(lag_mod)
## [1] 0.8789056
mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])
all_tot_pred <-
all_tot %>%
filter(!is.na(note_lag)) %>%
mutate(pred = mod_fit$fit,
pred.se = mod_fit$se.fit,
low = exp(pred - 1.96*pred.se),
hi = exp(pred + 1.96*pred.se))
glm_fit <- all_tot_pred %>%
filter(!is.na(note_lag)) %>%
ggplot(aes(x = note_lag, y = deaths)) +
geom_point() +
geom_line(aes(y = exp(pred))) +
geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
theme_bw() +
labs(y = "Daily number of\ndeaths reported",
x = "Daily number of NHS Pathways reports") +
large_txt
glm_fit
4 Supplementary figures
4.1 Serial interval distribution
This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.
SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale, w = 0.5)
SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
meanlog = log(4.7),
sdlog = log(2.9), w = 0.5)
SI_dist1 <- data.frame(x = SI_distribution$r(1e5))
SI_dist1 <- count(SI_dist1, x) %>%
ggplot() +
geom_col(aes(x = x, y = n)) +
labs(x = "Serial interval (days)", y = "Frequency") +
scale_x_continuous(breaks = seq(0, 30, 5)) +
theme_bw()
SI_dist2 <- data.frame(x = SI_distribution2$r(1e5))
SI_dist2 <- count(SI_dist2, x) %>%
ggplot() +
geom_col(aes(x = x, y = n)) +
labs(x = "Serial interval (days)", y = "Frequency") +
scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
theme_bw()
ggpubr::ggarrange(SI_dist1,
SI_dist2,
nrow = 1,
labels = "AUTO") 
4.2 Sensitivity analysis - 7 or 21 days moving window
We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.
First with the 7 days window:
## set moving time window (1/2/3 weeks)
w <- 7
# create empty df
r_all_sliding_7days <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_7days %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)plot_R <- r_all_sliding_7days %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_7days %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_7days %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R_7 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))Then with the 21 days window:
## set moving time window (1/2/3 weeks)
w <- 21
# create empty df
r_all_sliding_21days <- NULL
## make data for model
x_model_all_moving <- x %>%
filter(!is.na(nhs_region)) %>%
group_by(date, nhs_region) %>%
summarise(n = sum(count))
unique_dates <- unique(x_model_all_moving$date)
for (i in 1:(length(unique_dates) - w)) {
date_i <- unique_dates[i]
date_i_max <- date_i + w
model_data <- x_model_all_moving %>%
filter(date >= date_i & date < date_i_max) %>%
mutate(day = as.integer(date - date_i)) %>%
day_of_week()
mod <- glm(n ~ day * nhs_region + day_of_week,
data = model_data,
family = 'quasipoisson')
# get growth rate
r <- get_r(mod)
r$w_min <- date_i
r$w_max <- date_i_max
# combine all estimates
r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
}
#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
shape = SI_param$shape,
scale = SI_param$scale,
w = 0.5)
#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
mutate(R = epitrix::r2R0(r, SI_distribution),
R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))# plot
plot_growth <-
r_all_sliding_21days %>%
ggplot(aes(x = w_max, y = r)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 0, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated daily growth rate (r)") +
scale_colour_manual(values = pal)# plot
plot_R <-
r_all_sliding_21days %>%
ggplot(aes(x = w_max, y = R)) +
geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(yintercept = 1, linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "",
y = "Estimated effective reproduction\nnumber (Re)") +
scale_colour_manual(values = pal)
R <- r_all_sliding_21days %>%
mutate(lower_95 = R_lower_95,
upper_95 = R_upper_95,
value = R,
measure = "R",
reference = 1)
r_R <- r_all_sliding_21days %>%
mutate(measure = "r",
value = r,
reference = 0) %>%
bind_rows(R)
r_R_21 <- r_R %>%
ggplot(aes(x = w_max, y = value)) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
geom_line(aes(colour = nhs_region)) +
geom_point(aes(colour = nhs_region)) +
geom_hline(aes(yintercept = reference), linetype = "dashed") +
theme_bw() +
scale_weeks +
theme(legend.position = "bottom",
plot.margin = margin(0.5,1,0,0, "cm"),
strip.background = element_blank(),
strip.placement = "outside"
) +
guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
labs(x = "", y = "") +
scale_colour_manual(values = pal) +
facet_grid(rows = vars(measure),
scales = "free_y",
switch = "y",
labeller = as_labeller(c(r = "Daily growth rate (r)",
R = "Effective reproduction\nnumber (Re)")))And we combine both outputs into a single plot:
ggpubr::ggarrange(r_R_7,
r_R_21,
nrow = 2,
labels = "AUTO",
common.legend = TRUE,
legend = "bottom") 
4.3 Correlation between NHS Pathways reports and deaths by NHS region
lag_cor_reg <- data.frame()
for (i in 0:30) {
summary <-
all_data %>%
group_by(nhs_region) %>%
mutate(note_lag = lag(count, i)) %>%
## calculate rank correlation and bootstrap CI for each region
group_modify(~getboot(.x)) %>%
mutate(lag = i)
lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}
cor_vs_lag_reg <-
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
geom_hline(yintercept = 0, lty = "longdash") +
geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
geom_point() +
geom_line() +
facet_wrap(~nhs_region) +
scale_color_manual(values = pal) +
scale_fill_manual(values = pal, guide = F) +
theme_bw() +
labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
theme(legend.position = "bottom") +
guides(color = guide_legend(override.aes = list(fill = NA)))
cor_vs_lag_reg
5 Export data
We save the tables created during our analysis:
if (!dir.exists("excel_tables")) {
dir.create("excel_tables")
}
## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")
for (e in tables_to_export) {
rio::export(get(e),
file.path("excel_tables",
paste0(e, ".xlsx")))
}
## also export result from regression on lagged data
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))6 System information
6.1 Outline
The following information documents the system on which the document was compiled.
6.2 System
This provides information on the operating system.
6.3 R environment
This provides information on the version of R used:
6.4 R packages
This provides information on the packages used:
sessionInfo()
## R version 3.6.3 (2020-02-29)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS Catalina 10.15.4
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] ggnewscale_0.4.1 ggpubr_0.3.0 lubridate_1.7.8
## [4] chngpt_2020.5-21 cyphr_1.1.0 DT_0.13
## [7] kableExtra_1.1.0 janitor_2.0.1 remotes_2.1.1
## [10] projections_0.4.1 earlyR_0.0.1 epitrix_0.2.2
## [13] distcrete_1.0.3 incidence_1.7.1 rio_0.5.16
## [16] reshape2_1.4.4 rvest_0.3.5 xml2_1.3.2
## [19] linelist_0.0.40.9000 forcats_0.5.0 stringr_1.4.0
## [22] dplyr_0.8.5 purrr_0.3.4 readr_1.3.1
## [25] tidyr_1.1.0 tibble_3.0.1 ggplot2_3.3.0
## [28] tidyverse_1.3.0 here_0.1 reportfactory_0.0.5
##
## loaded via a namespace (and not attached):
## [1] colorspace_1.4-1 selectr_0.4-2 ggsignif_0.6.0 ellipsis_0.3.1
## [5] rprojroot_1.3-2 snakecase_0.11.0 fs_1.4.1 rstudioapi_0.11
## [9] farver_2.0.3 fansi_0.4.1 splines_3.6.3 knitr_1.28
## [13] jsonlite_1.6.1 broom_0.5.6 dbplyr_1.4.3 compiler_3.6.3
## [17] httr_1.4.1 backports_1.1.7 assertthat_0.2.1 Matrix_1.2-18
## [21] cli_2.0.2 htmltools_0.4.0 prettyunits_1.1.1 tools_3.6.3
## [25] gtable_0.3.0 glue_1.4.1 Rcpp_1.0.4.6 carData_3.0-4
## [29] cellranger_1.1.0 vctrs_0.3.0 nlme_3.1-144 matchmaker_0.1.1
## [33] crosstalk_1.1.0.1 xfun_0.14 ps_1.3.3 openxlsx_4.1.5
## [37] lifecycle_0.2.0 rstatix_0.5.0 MASS_7.3-51.5 scales_1.1.1
## [41] hms_0.5.3 sodium_1.1 yaml_2.2.1 curl_4.3
## [45] gridExtra_2.3 stringi_1.4.6 kyotil_2019.11-22 boot_1.3-24
## [49] pkgbuild_1.0.8 zip_2.0.4 rlang_0.4.6 pkgconfig_2.0.3
## [53] evaluate_0.14 lattice_0.20-38 labeling_0.3 htmlwidgets_1.5.1
## [57] cowplot_1.0.0 processx_3.4.2 tidyselect_1.1.0 plyr_1.8.6
## [61] magrittr_1.5 R6_2.4.1 generics_0.0.2 DBI_1.1.0
## [65] pillar_1.4.4 haven_2.3.0 foreign_0.8-75 withr_2.2.0
## [69] mgcv_1.8-31 survival_3.1-8 abind_1.4-5 modelr_0.1.8
## [73] crayon_1.3.4 car_3.0-8 utf8_1.1.4 rmarkdown_2.1
## [77] viridis_0.5.1 grid_3.6.3 readxl_1.3.1 data.table_1.12.8
## [81] callr_3.4.3 reprex_0.3.0 digest_0.6.25 webshot_0.5.2
## [85] munsell_0.5.0 viridisLite_0.3.0